TAP 521-7: Rutherford Scattering Data

TAP 521-7: Rutherford scattering data

The idea of scattering using Coulomb’s law and a small central positive charge for the atom was communicated to the Manchester Literary and Philosophical Society in February 1911. His ideas require that “the scattering due to a single atomic encounter is small” and that “it be supposed that the diameter of the sphere of positive electricity is minute compared with the diameter and sphere of influence of the atom”.

The table below shows some of Geiger and Marsden’s results

Counting was carried out for the same time at each angle

deflected angle 
degrees / number scattered
15.0 / 132,000
22.5 / 27,300
30.0 / 7,800
37.5 / 3,300
45.0 / 1,457
60.0 / 477
75.0 / 211
105 / 70
120 / 52
135 / 43
150 / 33

The actual formula

Number of  particles y falling on unit area deflected by angle is given by: -

where Q is the total number of particles falling on the scattering material, t is the thickness of the material, n the number of atoms within unit volume of the material, and b given by the formula below. N is the number of positive charges, e the size of the positive charge, m the mass of an  particle, u their velocity and E the charge of the  particle.

One of Rutherford’s conclusions was that the number of scintillations per unit area of zinc sulphide screen is proportional to

Maths note cosec ( 1/sin (

What to do

Add extra columns to the table as needed to enable you to draw a graph to test Rutherford’s conclusion that the number of scintillations per unit area of zinc sulphide screen is proportional to

As an extension you might like to plot number scattered against 1/4

Write down you conclusions from the graph(s)

Practical advice

Some students might like to see Rutherford’s equation and try a test to see how the results come out. This activity is considered optional. Some websites with papers of the time are given below for interest

Alternative approaches

A spreadsheet could be used for this activity.

You should find:

To a reasonable degree y proportional to
number scattered against 1/4 is only proportional at small angles.

External references

This activity is based on “The Scattering of and Particles By Matter and the Structure of the Atom. By Professor E RUTHERFORD F.R.S., University of Manchester.“ from which the equation is quoted and the section in quotation marks at the top of the page.

An abstract of the paper is at: -